It takes a much smaller TCB, and no connection state, to AAA a signed request, but with mutual-auth you need a state machine and the TCBs for X509/ASN.1 validation tend to be huge. That's not what you want in a security critical control. Honestly, enabling normal TLS mutual-auth likely degrades security in most cases, as it opens the server to whatever attacks the X509 processing is vulnerable to. ALTS mitigates this somewhat by using Protobufs, but that's still a very very big TCB. Compare that to say the TCB for validating HMAC or ed25519.
Then there's the basic stuff I already pointed out, like sessions lasting longer than their credentials are valid for. The layering violation invites these kind of issues.
Mutual auth increases the TCB by a lot, the Kolmogorov complexity increases by several orders of magnitude.
(For the record in BeyondCorp all backend components are mutually authenticated but they still use sessions and U2F tokens so there are no trusted points).